You should study. You still have to have the chops to pass a full-day onsite. Having a contact from your network trying to bring you in just cuts down on the amount of pointless hoop-jumping.
Building and maintaining a professional network is something you should be doing all the time. If you wait until you need a job to network you are doing it wrong.
Well then I must be doing it wrong because all I want to do after work is relax and not talk to anyone and sometimes play video games. I still want to be recognized for the work that I do but apparently that's not enough.
Maybe I have Asperger's or something else, but this whole thing about relying on connections to get jobs more easily doesn't come naturally to me.
Building and maintaining a professional network is something you should be doing all the time. If you wait until you need a job to network you are doing it wrong.